US20120232847A1 - High Accuracy And High Dynamic Range MEMS Inertial Measurement Unit With Automatic Dynamic Range Control - Google Patents
High Accuracy And High Dynamic Range MEMS Inertial Measurement Unit With Automatic Dynamic Range Control Download PDFInfo
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- US20120232847A1 US20120232847A1 US13/044,191 US201113044191A US2012232847A1 US 20120232847 A1 US20120232847 A1 US 20120232847A1 US 201113044191 A US201113044191 A US 201113044191A US 2012232847 A1 US2012232847 A1 US 2012232847A1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/166—Mechanical, construction or arrangement details of inertial navigation systems
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
- G01C19/56—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces
- G01C19/5776—Signal processing not specific to any of the devices covered by groups G01C19/5607 - G01C19/5719
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/183—Compensation of inertial measurements, e.g. for temperature effects
- G01C21/188—Compensation of inertial measurements, e.g. for temperature effects for accumulated errors, e.g. by coupling inertial systems with absolute positioning systems
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
- G01P15/02—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses
- G01P15/08—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values
- G01P15/0802—Details
Definitions
- This invention relates generally to the field of guidance, navigation, and control systems and specifically to inertial measurement units.
- IMUs inertial measurement units
- quartz accelerometers, fiber optical gyroscopes, and/or laser gyroscopes have been conventionally used.
- quartz accelerometers, fiber optical gyroscopes, and/or laser gyroscopes have drawbacks as well.
- IMUs based on these technologies are relatively expensive, large in size, and heavy in power consumption, as compared to micro-electro-mechanical systems (MEMS) IMUs.
- MEMS micro-electro-mechanical systems
- the IMU In current low cost IMUs, such as MEMS IMUs, the IMU either has high accuracy or has high dynamic measurement range.
- the invention disclosed herein addresses the need for a low cost IMU that has both high accuracy and high dynamic range.
- Embodiments relate to a MEMS IMU having an automatic gain control.
- the dynamic measurement range of the MEMS IMU is controlled by controlling the gain of a signal amplifier that amplifies the signal before the signal reaches an analog to digital converter (ADC) in order to make full use of the ADC range.
- ADC analog to digital converter
- Measurements of the vehicle dynamics can be determined by digital circuits or a processor. Then, the measurements can be used as feedback to control the gain of the amplifier.
- ADC analog to digital converter
- two or more MEMS inertial sensor sets are installed in the IMU.
- One of the sensor sets is for high accuracy with low dynamic range, and the other set or sets is for higher dynamic range with less resolution or accuracy.
- a digital processor determines which of the sensor sets to be used according to the system dynamic estimation.
- the system weights the sensor outputs from the sensor sets according to the system dynamics.
- FIG. 1 is a block diagram illustrating a system including automatic gain control to increase IMU dynamic range, according to one embodiment of the invention.
- FIG. 2A is a block diagram illustrating a first example system for adaptive sensor choice for analog sensors, according to one embodiment of the invention.
- FIG. 2B is a block diagram illustrating a second example system for adaptive sensor choice for analog sensors, according to one embodiment of the invention.
- FIG. 2C is a block diagram illustrating a third example system for adaptive sensor choice for analog sensors, according to one embodiment of the invention.
- FIG. 3 is a block diagram illustrating an example system for adaptive sensor choice for digital sensors, according to one embodiment of the invention.
- FIG. 4 is a block diagram illustrating a dynamically weighted multi-sensor IMU using analog inertial sensors, according to one embodiment of the invention.
- FIG. 5 is a block diagram illustrating a dynamically weighted multi-sensor IMU using digital inertial sensors, according to one embodiment of the invention.
- FIG. 1 is a block diagram illustrating a system 100 in accordance with an embodiment of the invention.
- the system 100 includes at least one inertial sensor 110 , an automatic gain control amplifier 120 , an analog to digital converter 130 , and a digital signal processing unit 140 .
- the system 100 may be placed, for example, inside a land vehicle, an aerospace vehicle, or any other moveable object.
- the one or more inertial sensor 110 measures the inertial forces present as the system 100 moves. Measurement signals representative of the inertial forces are output from the one or more inertial sensor 110 to the automatic gain control amplifier 120 .
- the automatic gain control amplifier 120 receives the measurement signals from the inertial sensor 110 and amplifies the measurement signal according to a gain amount that varies based on the automatic gain control feedback 150 .
- the output of the automatic gain control amplifier 120 is transmitted to the ADC 130 .
- the ADC 130 receives the amplified analog signals from the automatic gain control amplifier 120 and converts them to digital signals. The digital output of the ADC 130 is then conveyed to the digital signal processing unit 140 .
- the digital signal processing unit 140 receives the digital output from the ADC 130 and processes the signals, in some embodiments, to determine the motion of the system 100 based on the inertial forces measured by the inertial sensor 110 .
- the digital signal processing unit 140 can be an electronic circuit or a standard digital processor/controller, for example.
- the digital signal processing unit 140 may also output an automatic gain control feedback 150 to control the gain of the automatic gain control amplifier 120 , for example, in a linear or stepwise manner. In linear control mode, the gain of the amplifier 120 is reversely proportional to the dynamics to keep the input analog signal to an optimal percentage of the ADC input range to maximize the signal to noise ration, such as around 70% in most of applications.
- the implementation of the AGC circuits are simpler than the in the linear mode, and sub optimization can be achieved. Accordingly, the full use of the range of the ADC 130 increases the resolution in low dynamic conditions and increases the measurement range in high dynamic conditions. A further advantage of this implementation is that the number of sensors is not increased in order to achieve these results.
- FIG. 2A is a block diagram illustrating a first example system for adaptive sensor choice for analog sensors, according to one embodiment of the invention.
- the system 201 includes a plurality of analog sensors, a multiplexer (MUX) 221 , a signal conditioning module 222 , an ADC 130 , and a digital signal processing unit 140 .
- MUX multiplexer
- the plurality of analog sensors (labeled 1 through N) measure the inertial forces present as the system 201 moves. In some implementations, as few as two sensors are used, and in other implementations, any number up to one hundred sensors or more can be used. In one embodiment, the plurality of analog sensors each of which has a different measurement range. The ranges of individual sensors of the plurality may partially overlap in some embodiments. In one embodiment, the measurement range of a first sensor contains portion that is not present in the measurement range of a second sensor. In another embodiment, the measurement range of a first sensor contains portion that is not present in the measurement range of a second sensor, and vice versa. Measurement signals representative of the inertial forces are output from the analog sensors to the MUX 221 .
- the MUX 221 is used to switch between the analog sensors 1 through N, according to a control referred to herein as the adaptive sensor choice 250 .
- the adaptive sensor choice 250 comprises the digital signal processing unit 140 and the MUX 221 .
- the digital signal processing unit 140 determines the dynamics of the motion and sends the command/signal to the MUX 221 to choose the analog sensor which is the best of the sensor array to work in this dynamic range.
- the MUX 221 transmits the signals received from the selected analog sensor to a signal conditioning module 222 .
- the signal conditioning module 222 is used to amplify and filter the analog signal.
- the signal conditioning module 222 receives the analog signal from the MUX 221 , and transmits the amplified and/or filtered signal to the ADC 130 .
- the ADC 130 receives the analog signal from the signal conditioning module 222 and converts it to a digital signal. The ADC 130 then outputs the digital signal to the digital signal processing unit 140 .
- the digital signal processing unit 140 processes the digital signal from the ADC 130 .
- the digital signal processing unit 140 also determines which sensor to be used according to the estimated system dynamics and sends control signals, referred to in FIG. 2A as an adaptive sensor choice 250 , to the MUX 221 .
- the adaptive sensor choice 250 signals the MUX 221 to select an analog sensor from the plurality of analog sensors 1 -N with high accuracy and low measurement range.
- the adaptive sensor choice 250 signals the MUX 221 to select an analog sensor with a high measurement range to avoid saturation of the sensor with low measurement range.
- An advantage of the implementation of FIG. 2A is that the plurality of sensors allows the selection of the sensor to be tailored to the situation. Some sensor technologies perform best in low dynamic cases. Some sensor technologies perform best at high dynamics. Embodiment of the invention to use a combination of these sensor technologies to achieve the best system performance over a wide range of system dynamics.
- FIG. 2B is a block diagram illustrating a second example system 202 for adaptive sensor choice for analog sensors, according to one embodiment of the invention.
- FIG. 2B is a variation of the system 201 of FIG. 2A .
- the signal conditioning module 222 is optionally excluded.
- the MUX 221 outputs a signal that is received by the ADC 130 .
- Advantages of this arrangement include the presence of few components and a lower manufacturing cost.
- the ADC sampling rate needs to be at least twice as the sensor signal bandwidth to avoid aliasing. Some of the MEMS sensors can be set to a certain bandwidth to meet this requirement.
- the digital signal processing unit 140 can also be used to perform digital filtering.
- FIG. 2C is a block diagram illustrating a third example system 203 for adaptive sensor choice for analog sensors, according to one embodiment of the invention.
- FIG. 2C is another variation of the system 201 of FIG. 2A .
- signal conditioning is performed by a plurality of modules 222 A- 222 N, one positioned between each analog sensor and the MUX 221 .
- An advantage of this arrangement is that a signal conditioning module is devoted to each particular sensor, and thus can be optimized for peak performance from the corresponding sensor.
- FIG. 3 is a block diagram illustrating an example system 301 for adaptive sensor choice for digital sensors, according to one embodiment of the invention.
- FIG. 3 is another variation of FIG. 2A , but in the system 301 , digital inertial sensors 1 -N are used in the inertial measurement unit instead of analog sensors.
- the advantage of using digital sensors is the simplicity of the circuitry. No analog circuits are required except for the power supply. Hence, the system can have smaller form of factor.
- FIG. 4 is a block diagram illustrating a dynamically weighted multi-sensor IMU system 401 using analog inertial sensors, according to one embodiment of the invention.
- the system 401 includes two or more analog sensors, an ADC 130 , and a digital signal processing unit 140 .
- the two or more analog sensors at least one of them achieves its best performance in low dynamic situations, and at least one of the other sensors achieves its best performance in high dynamic situations.
- All the analog signal sensor output is routed through an ADC 130 and collected by the digital signal processing unit 140 .
- the sensor measurements are weighted at the digital signal processing unit 140 depending on the performance characteristics of the individual sensors and the system 401 motion dynamics. In general, more weight is given to the sensor or sensors that have a range appropriate for the measurement. For example:
- x is the weighted measurement and w i is the weighting factor for the measurement ⁇ tilde over (x) ⁇ i .
- FIG. 5 is a block diagram illustrating a dynamically weighted multi-sensor IMU system 501 using digital inertial sensors, according to one embodiment of the invention.
- FIG. 5 is a variation of FIG. 4 , but in this system 501 , digital inertial sensors 1 -N are used in the inertial measurement unit instead of analog sensors. In this embodiment, there is no ADC external to the sensors. Hence, a smaller form of factor can be achieved.
- Advantages of the implementations illustrated in FIGS. 4 and 5 are that a better overall performance of the inertial measurement systems can be achieved through a combination of measurements in the digital signal processing unit.
- the combination of measurements from the sensors reduces the noise level and random walk error by the square root of N times within the overlapping sensor measurement range, wherein N is the number of sensors participating in the measurement.
- Another benefit of using a combination of measurements from multiple sensors is a reduction in the effects of artifacts caused by switching between sensors.
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Abstract
Description
- This invention relates generally to the field of guidance, navigation, and control systems and specifically to inertial measurement units.
- Guidance, navigation, and control systems, such as land vehicle, aerospace, and military inertial systems, require inertial measurement units (IMUs) that have both high accuracy and high dynamic range. To meet the high accuracy and high dynamic range requirements, quartz accelerometers, fiber optical gyroscopes, and/or laser gyroscopes have been conventionally used. However, the use of quartz accelerometers, fiber optical gyroscopes, and/or laser gyroscopes have drawbacks as well. Specifically, IMUs based on these technologies are relatively expensive, large in size, and heavy in power consumption, as compared to micro-electro-mechanical systems (MEMS) IMUs.
- In current low cost IMUs, such as MEMS IMUs, the IMU either has high accuracy or has high dynamic measurement range. The invention disclosed herein addresses the need for a low cost IMU that has both high accuracy and high dynamic range.
- Embodiments relate to a MEMS IMU having an automatic gain control. The dynamic measurement range of the MEMS IMU is controlled by controlling the gain of a signal amplifier that amplifies the signal before the signal reaches an analog to digital converter (ADC) in order to make full use of the ADC range. Measurements of the vehicle dynamics can be determined by digital circuits or a processor. Then, the measurements can be used as feedback to control the gain of the amplifier. Thus, high dynamic measurement range is achieved, and the accuracy is increased when the system is in low dynamic motion.
- In one embodiment, two or more MEMS inertial sensor sets are installed in the IMU. One of the sensor sets is for high accuracy with low dynamic range, and the other set or sets is for higher dynamic range with less resolution or accuracy. In one implementation, a digital processor determines which of the sensor sets to be used according to the system dynamic estimation. In another implementation, the system weights the sensor outputs from the sensor sets according to the system dynamics.
-
FIG. 1 is a block diagram illustrating a system including automatic gain control to increase IMU dynamic range, according to one embodiment of the invention. -
FIG. 2A is a block diagram illustrating a first example system for adaptive sensor choice for analog sensors, according to one embodiment of the invention. -
FIG. 2B is a block diagram illustrating a second example system for adaptive sensor choice for analog sensors, according to one embodiment of the invention. -
FIG. 2C is a block diagram illustrating a third example system for adaptive sensor choice for analog sensors, according to one embodiment of the invention. -
FIG. 3 is a block diagram illustrating an example system for adaptive sensor choice for digital sensors, according to one embodiment of the invention. -
FIG. 4 is a block diagram illustrating a dynamically weighted multi-sensor IMU using analog inertial sensors, according to one embodiment of the invention. -
FIG. 5 is a block diagram illustrating a dynamically weighted multi-sensor IMU using digital inertial sensors, according to one embodiment of the invention. - Embodiments of the invention employ automatic gain control to an inertial system to achieve high dynamic measurement range and to increase the accuracy when the system is in low dynamic motion.
FIG. 1 is a block diagram illustrating asystem 100 in accordance with an embodiment of the invention. Thesystem 100 includes at least oneinertial sensor 110, an automaticgain control amplifier 120, an analog todigital converter 130, and a digitalsignal processing unit 140. Thesystem 100 may be placed, for example, inside a land vehicle, an aerospace vehicle, or any other moveable object. - The one or more
inertial sensor 110 measures the inertial forces present as thesystem 100 moves. Measurement signals representative of the inertial forces are output from the one or moreinertial sensor 110 to the automaticgain control amplifier 120. - The automatic
gain control amplifier 120 receives the measurement signals from theinertial sensor 110 and amplifies the measurement signal according to a gain amount that varies based on the automatic gain control feedback 150. The output of the automaticgain control amplifier 120 is transmitted to the ADC 130. - The ADC 130 receives the amplified analog signals from the automatic
gain control amplifier 120 and converts them to digital signals. The digital output of the ADC 130 is then conveyed to the digitalsignal processing unit 140. - The digital
signal processing unit 140 receives the digital output from theADC 130 and processes the signals, in some embodiments, to determine the motion of thesystem 100 based on the inertial forces measured by theinertial sensor 110. The digitalsignal processing unit 140 can be an electronic circuit or a standard digital processor/controller, for example. The digitalsignal processing unit 140 may also output an automatic gain control feedback 150 to control the gain of the automaticgain control amplifier 120, for example, in a linear or stepwise manner. In linear control mode, the gain of theamplifier 120 is reversely proportional to the dynamics to keep the input analog signal to an optimal percentage of the ADC input range to maximize the signal to noise ration, such as around 70% in most of applications. In the stepwise mode, the implementation of the AGC circuits are simpler than the in the linear mode, and sub optimization can be achieved. Accordingly, the full use of the range of theADC 130 increases the resolution in low dynamic conditions and increases the measurement range in high dynamic conditions. A further advantage of this implementation is that the number of sensors is not increased in order to achieve these results. -
FIG. 2A is a block diagram illustrating a first example system for adaptive sensor choice for analog sensors, according to one embodiment of the invention. In this example, thesystem 201 includes a plurality of analog sensors, a multiplexer (MUX) 221, asignal conditioning module 222, anADC 130, and a digitalsignal processing unit 140. - The plurality of analog sensors (labeled 1 through N) measure the inertial forces present as the
system 201 moves. In some implementations, as few as two sensors are used, and in other implementations, any number up to one hundred sensors or more can be used. In one embodiment, the plurality of analog sensors each of which has a different measurement range. The ranges of individual sensors of the plurality may partially overlap in some embodiments. In one embodiment, the measurement range of a first sensor contains portion that is not present in the measurement range of a second sensor. In another embodiment, the measurement range of a first sensor contains portion that is not present in the measurement range of a second sensor, and vice versa. Measurement signals representative of the inertial forces are output from the analog sensors to the MUX 221. - The MUX 221 is used to switch between the
analog sensors 1 through N, according to a control referred to herein as theadaptive sensor choice 250. Theadaptive sensor choice 250 comprises the digitalsignal processing unit 140 and the MUX 221. The digitalsignal processing unit 140 determines the dynamics of the motion and sends the command/signal to the MUX 221 to choose the analog sensor which is the best of the sensor array to work in this dynamic range. In response to theadaptive sensor choice 250, the MUX 221 transmits the signals received from the selected analog sensor to asignal conditioning module 222. - The
signal conditioning module 222 is used to amplify and filter the analog signal. Thesignal conditioning module 222 receives the analog signal from theMUX 221, and transmits the amplified and/or filtered signal to theADC 130. - The ADC 130 receives the analog signal from the
signal conditioning module 222 and converts it to a digital signal. TheADC 130 then outputs the digital signal to the digitalsignal processing unit 140. - The digital
signal processing unit 140 processes the digital signal from theADC 130. The digitalsignal processing unit 140 also determines which sensor to be used according to the estimated system dynamics and sends control signals, referred to inFIG. 2A as anadaptive sensor choice 250, to theMUX 221. When thesystem 201 is in low dynamic situations, theadaptive sensor choice 250 signals theMUX 221 to select an analog sensor from the plurality of analog sensors 1-N with high accuracy and low measurement range. In high dynamic situations, theadaptive sensor choice 250 signals theMUX 221 to select an analog sensor with a high measurement range to avoid saturation of the sensor with low measurement range. - An advantage of the implementation of
FIG. 2A is that the plurality of sensors allows the selection of the sensor to be tailored to the situation. Some sensor technologies perform best in low dynamic cases. Some sensor technologies perform best at high dynamics. Embodiment of the invention to use a combination of these sensor technologies to achieve the best system performance over a wide range of system dynamics. -
FIG. 2B is a block diagram illustrating asecond example system 202 for adaptive sensor choice for analog sensors, according to one embodiment of the invention.FIG. 2B is a variation of thesystem 201 ofFIG. 2A . In this variation, thesignal conditioning module 222 is optionally excluded. Instead, theMUX 221 outputs a signal that is received by theADC 130. Advantages of this arrangement include the presence of few components and a lower manufacturing cost. In this embodiment, the ADC sampling rate needs to be at least twice as the sensor signal bandwidth to avoid aliasing. Some of the MEMS sensors can be set to a certain bandwidth to meet this requirement. The digitalsignal processing unit 140 can also be used to perform digital filtering. -
FIG. 2C is a block diagram illustrating athird example system 203 for adaptive sensor choice for analog sensors, according to one embodiment of the invention.FIG. 2C is another variation of thesystem 201 ofFIG. 2A . In this variation, signal conditioning is performed by a plurality ofmodules 222A-222N, one positioned between each analog sensor and theMUX 221. An advantage of this arrangement is that a signal conditioning module is devoted to each particular sensor, and thus can be optimized for peak performance from the corresponding sensor. -
FIG. 3 is a block diagram illustrating anexample system 301 for adaptive sensor choice for digital sensors, according to one embodiment of the invention.FIG. 3 is another variation ofFIG. 2A , but in thesystem 301, digital inertial sensors 1-N are used in the inertial measurement unit instead of analog sensors. The advantage of using digital sensors is the simplicity of the circuitry. No analog circuits are required except for the power supply. Hence, the system can have smaller form of factor. -
FIG. 4 is a block diagram illustrating a dynamically weightedmulti-sensor IMU system 401 using analog inertial sensors, according to one embodiment of the invention. Thesystem 401 includes two or more analog sensors, anADC 130, and a digitalsignal processing unit 140. - In the example of
FIG. 4 , of the two or more analog sensors, at least one of them achieves its best performance in low dynamic situations, and at least one of the other sensors achieves its best performance in high dynamic situations. All the analog signal sensor output is routed through anADC 130 and collected by the digitalsignal processing unit 140. However, in contrast to the embodiments described above, in this embodiment, the sensor measurements are weighted at the digitalsignal processing unit 140 depending on the performance characteristics of the individual sensors and thesystem 401 motion dynamics. In general, more weight is given to the sensor or sensors that have a range appropriate for the measurement. For example: -
- Where x is the weighted measurement and wi is the weighting factor for the measurement {tilde over (x)}i.
-
FIG. 5 is a block diagram illustrating a dynamically weightedmulti-sensor IMU system 501 using digital inertial sensors, according to one embodiment of the invention.FIG. 5 is a variation ofFIG. 4 , but in thissystem 501, digital inertial sensors 1-N are used in the inertial measurement unit instead of analog sensors. In this embodiment, there is no ADC external to the sensors. Hence, a smaller form of factor can be achieved. - Advantages of the implementations illustrated in
FIGS. 4 and 5 are that a better overall performance of the inertial measurement systems can be achieved through a combination of measurements in the digital signal processing unit. The combination of measurements from the sensors reduces the noise level and random walk error by the square root of N times within the overlapping sensor measurement range, wherein N is the number of sensors participating in the measurement. Another benefit of using a combination of measurements from multiple sensors is a reduction in the effects of artifacts caused by switching between sensors. - Although the detailed description contains many specifics, these should not be construed as limiting the scope of the invention, but merely as illustrating different examples and aspects of the invention. It should be appreciated that the scope of the invention includes other embodiments not discussed in detail above. Various other modifications, changes and variations which will be apparent to those skilled in the art may be made in the arrangement and details of the apparatus and methods of the invention disclosed herein without departing from the spirit and scope of the invention.
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